explain xkcd - User contributions [en]

2586: Greek Letters

2022-02-26T08:43:40Z

WilliamJWatson: /* Explanation */ Added "angular frequency" to explanation of lower case omega.

{{comic
| number = 2586
| date = February 25, 2022
| title = Greek Letters
| image = greek_letters.png
| titletext = If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.
}}

==Explanation==
{{incomplete|Created by '''''O R B S''''' PRO®- Missing explanations for some letters. Do NOT delete this tag too soon.}}

Mathematics uses lots of Greek letters, typically using {{w|Greek_letters_used_in_mathematics,_science,_and_engineering|the same letter consistently}} to represent a particular constant or type of variable.
This comic gives a (non-)explanation of what they typically mean.

The letters are:

* '''π (lower-case pi)''' — Typically used to refer to the constant ratio between a circle’s circumference and its diameter (approximately 3.14). This usage of pi commonly applies to equations in introductory geometry classes, which would be considered "simple" by advanced mathematicians. However, pi also shows up seemingly randomly in extremely advanced and complicated equations (that have nothing to do with a circle), as part of the solution to an infinite series or whatnot. (There are also {{w|Pi_(letter)#Lowercase_Pi|several advanced equations}} which use pi to represent variables other than the ratio of the circumference to the diameter.)

* '''Δ (capital delta)''' — Typically used to refer to a change in quantity.

* '''δ (lower-case delta)''' — Also typically used to refer to a change in quantity, but unlike the capital delta, this is only for infinitesimal changes and is used in derivative and integration expressions in mathematics hence the text's reference to "a mathematician's fault".

* '''θ (lower-case theta)''' — Typically used to refer to an angle, and is notably used in the polar coordinate system. The text refers to its close relationship with circles, on which the polar coordinate system is based on.

* '''Φ (lower-case phi)''' — Typically used to refer to another angle other than one referred to by theta. It's used in spherical coordinates, and the text refers to how spheres, or orbs, are important in spherical coordinates.

* '''ϵ (lower-case lunate epsilon)''' — Epsilon is typically used to refer to very small quantities which go to zero in the limit. In this interpretation, the comic suggests that because these quantities are very small, they are unimportant, when in reality the study of quantities that go to zero gives rise to limits and calculus. It is also used for the series of transfinite numbers that are unreachable from ω (see below) using addition, multiplication, and exponentiation. Also used in statistical modelling to denote observational noise.

* '''υ,ν (lower-case upsilon and lower-case nu)''' — If these are being used it implies that the normal u & v characters are already assigned as constants or variables, and thus the math is probably of a higher level. Common in college level physics and engineering equations.

* '''μ (lower-case mu)''' — The SI prefix for "micro" = 10<sup>-6</sup>, representing very small quantities: a micrometer (μm) is tens of times smaller than the width of a human hair, a microgram (μg) is one single fine speck of flour, both of which are barely visible with the bare human eye nor feelable through the skin.

* '''Σ (capital sigma)''' — Typically used as a symbol for summation of a series of numbers.

* '''Π (capital pi)''' — Typically used as a symbol for multiplication of a series of numbers.

* '''ζ (lower-case zeta)''' — Frequently used with number theory, in particular the {{w|Riemann zeta function}}, which is a the focus of a famously unsolved problem in highly advanced mathematics.

* '''β (lower-case beta)''' — This could be a reference to the typical usage of beta to represent coefficients of independent variables in the {{w|Ordinary_least_squares#Linear_model|ordinary least squares regression model}}. Regression can potentially have a large number of independent variables, hence potentially many different betas (differentiated by subscript, or compacted into matrix notation) would be used. Alternatively, the comic might suggest whatever source this equation is from has run out of Latin letters to use as symbols, and is now going through the Greek letters.

* '''α (lower-case alpha)''' — Possibly referring to alpha radiation, which certainly could kill someone. Quite likely refers to angular acceleration, or the acceleration of spinning systems, which are capable of killing people in a number of [https://xkcd.com/123/ interesting ways]...

* '''Ω (capital omega)''' — This symbol has been used for a {{w|Omega_function|variety of mathematical functions}}. Also used for the symbol for {{w|ohms}}, a unit for electrical resistance, and for the first uncountable ordinal.

* '''ω (lower-case omega)''' — Lower-case omega is used for the {{w|Transfinite_number|lowest transfinite ordinal number}}, a specific way of referring to a type of infinity in a mathematically robust way. The line about dying here among the transfinite equations may be in reference to the literally infinite scope of the branch of mathematics. It is also used in physics and electrical engineering for angular frequency, equal to 2πf.

* '''σ (lower-case sigma)''' — In statistics, commonly refers to the standard deviation of a distribution. Statistics often attempts to use simplified models to explain real-world phenomena.

* '''ξ (lower-case xi)''' — Randall comments that this looks like a strand of curly hair. Xi is used in the {{w|Riemann Xi function}}.

* '''γ (lower-case gamma)''' — Gamma ray is the most powerful classification of electromagnetic radiation AKA "light", and powerful lights are frequently associated with high-tech, futuristic devices and weapons, hence "space noises". Alternatively, this might be a reference to the Lorentz factor, an important variable in special relativity calculations.

* '''ρ (lower-case rho)''' — often used to measure density, such as air density that a wing might be travelling through.

* '''Ξ (capital xi)''' — Resembles the icon of some {{w|Stack Exchange}} [https://stackexchange.com/sites# sites]. This character is also identical to Besh, the second letter of the {{w|Aurebesh Alphabet}} [https://starwars.fandom.com/wiki/Aurebesh].
* '''ψ (lower-case psi)''' — Psi looks exactly like a trident. This is hilarious.{{citation needed}} In quantum mechanics it's used to describe the wave function of a particle, leading to a bad pun. (Psi is also used in mathematics to represent the sum of the inverse of the Fibonacci numbers, the division polynomials, and the supergolden ratio.)

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Header:]
:What Greek letters mean in equations

:[What follows is a list of Greek letters, with explanations next to them.]
:π This math is either very simple or impossible.
:Δ Something has changed.
:δ Something has changed and it's a mathematician's fault.
:θ Circles!
:Φ '''''O R B S'''''
:ϵ Not important, don't worry about it.
:υ,ν Is that a V or a U? Or...oh no, it's one of ''those''.
:μ This math is cool but it's not about anything that you will ever see or touch, so whatever.
:Σ Thank you for purchasing ''Addition Pro''®!
:Π ...and the ''Multiplication''® expansion pack!
:ζ This math will only lead to more math.
:β There are just too many coefficients.
:α Oh boy, now '''''this''''' is math about something real. This is math that could '''''kill''''' someone.
:Ω Oooh, ''some'' mathematician thinks their function is cool and important.
:ω A lot of work went into these equations and you are going to die here among them.
:σ Some poor soul is trying to apply this math to real life and it's not working.
:ξ Either this is terrifying mathematics or there was a hair on the scanned page.
:γ ''Zoom'' pew pew pew [space noises] ''zoooom!''
:ρ Unfortunately, the test vehicle suffered an unexpected wing separation event.
:Ξ Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.
:ψ You have entered the domain of King Trition, ruler of the waves.

{{comic discussion}}
[[Category:Math]]
[[Category:Language]]

2586: Greek Letters

2022-02-26T08:41:05Z

WilliamJWatson: Added "for" to indicate that Ohms is independent from the first uncountable ordinal.

{{comic
| number = 2586
| date = February 25, 2022
| title = Greek Letters
| image = greek_letters.png
| titletext = If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.
}}

==Explanation==
{{incomplete|Created by '''''O R B S''''' PRO®- Missing explanations for some letters. Do NOT delete this tag too soon.}}

Mathematics uses lots of Greek letters, typically using {{w|Greek_letters_used_in_mathematics,_science,_and_engineering|the same letter consistently}} to represent a particular constant or type of variable.
This comic gives a (non-)explanation of what they typically mean.

The letters are:

* '''π (lower-case pi)''' — Typically used to refer to the constant ratio between a circle’s circumference and its diameter (approximately 3.14). This usage of pi commonly applies to equations in introductory geometry classes, which would be considered "simple" by advanced mathematicians. However, pi also shows up seemingly randomly in extremely advanced and complicated equations (that have nothing to do with a circle), as part of the solution to an infinite series or whatnot. (There are also {{w|Pi_(letter)#Lowercase_Pi|several advanced equations}} which use pi to represent variables other than the ratio of the circumference to the diameter.)

* '''Δ (capital delta)''' — Typically used to refer to a change in quantity.

* '''δ (lower-case delta)''' — Also typically used to refer to a change in quantity, but unlike the capital delta, this is only for infinitesimal changes and is used in derivative and integration expressions in mathematics hence the text's reference to "a mathematician's fault".

* '''θ (lower-case theta)''' — Typically used to refer to an angle, and is notably used in the polar coordinate system. The text refers to its close relationship with circles, on which the polar coordinate system is based on.

* '''Φ (lower-case phi)''' — Typically used to refer to another angle other than one referred to by theta. It's used in spherical coordinates, and the text refers to how spheres, or orbs, are important in spherical coordinates.

* '''ϵ (lower-case lunate epsilon)''' — Epsilon is typically used to refer to very small quantities which go to zero in the limit. In this interpretation, the comic suggests that because these quantities are very small, they are unimportant, when in reality the study of quantities that go to zero gives rise to limits and calculus. It is also used for the series of transfinite numbers that are unreachable from ω (see below) using addition, multiplication, and exponentiation. Also used in statistical modelling to denote observational noise.

* '''υ,ν (lower-case upsilon and lower-case nu)''' — If these are being used it implies that the normal u & v characters are already assigned as constants or variables, and thus the math is probably of a higher level. Common in college level physics and engineering equations.

* '''μ (lower-case mu)''' — The SI prefix for "micro" = 10<sup>-6</sup>, representing very small quantities: a micrometer (μm) is tens of times smaller than the width of a human hair, a microgram (μg) is one single fine speck of flour, both of which are barely visible with the bare human eye nor feelable through the skin.

* '''Σ (capital sigma)''' — Typically used as a symbol for summation of a series of numbers.

* '''Π (capital pi)''' — Typically used as a symbol for multiplication of a series of numbers.

* '''ζ (lower-case zeta)''' — Frequently used with number theory, in particular the {{w|Riemann zeta function}}, which is a the focus of a famously unsolved problem in highly advanced mathematics.

* '''β (lower-case beta)''' — This could be a reference to the typical usage of beta to represent coefficients of independent variables in the {{w|Ordinary_least_squares#Linear_model|ordinary least squares regression model}}. Regression can potentially have a large number of independent variables, hence potentially many different betas (differentiated by subscript, or compacted into matrix notation) would be used. Alternatively, the comic might suggest whatever source this equation is from has run out of Latin letters to use as symbols, and is now going through the Greek letters.

* '''α (lower-case alpha)''' — Possibly referring to alpha radiation, which certainly could kill someone. Quite likely refers to angular acceleration, or the acceleration of spinning systems, which are capable of killing people in a number of [https://xkcd.com/123/ interesting ways]...

* '''Ω (capital omega)''' — This symbol has been used for a {{w|Omega_function|variety of mathematical functions}}. Also used for the symbol for {{w|ohms}}, a unit for electrical resistance, and for the first uncountable ordinal.

* '''ω (lower-case omega)''' — Lower-case omega is used for the {{w|Transfinite_number|lowest transfinite ordinal number}}, a specific way of referring to a type of infinity in a mathematically robust way. The line about dying here among the transfinite equations may be in reference to the literally infinite scope of the branch of mathematics.

* '''σ (lower-case sigma)''' — In statistics, commonly refers to the standard deviation of a distribution. Statistics often attempts to use simplified models to explain real-world phenomena.

* '''ξ (lower-case xi)''' — Randall comments that this looks like a strand of curly hair. Xi is used in the {{w|Riemann Xi function}}.

* '''γ (lower-case gamma)''' — Gamma ray is the most powerful classification of electromagnetic radiation AKA "light", and powerful lights are frequently associated with high-tech, futuristic devices and weapons, hence "space noises". Alternatively, this might be a reference to the Lorentz factor, an important variable in special relativity calculations.

* '''ρ (lower-case rho)''' — often used to measure density, such as air density that a wing might be travelling through.

* '''Ξ (capital xi)''' — Resembles the icon of some {{w|Stack Exchange}} [https://stackexchange.com/sites# sites]. This character is also identical to Besh, the second letter of the {{w|Aurebesh Alphabet}} [https://starwars.fandom.com/wiki/Aurebesh].
* '''ψ (lower-case psi)''' — Psi looks exactly like a trident. This is hilarious.{{citation needed}} In quantum mechanics it's used to describe the wave function of a particle, leading to a bad pun. (Psi is also used in mathematics to represent the sum of the inverse of the Fibonacci numbers, the division polynomials, and the supergolden ratio.)

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Header:]
:What Greek letters mean in equations

:[What follows is a list of Greek letters, with explanations next to them.]
:π This math is either very simple or impossible.
:Δ Something has changed.
:δ Something has changed and it's a mathematician's fault.
:θ Circles!
:Φ '''''O R B S'''''
:ϵ Not important, don't worry about it.
:υ,ν Is that a V or a U? Or...oh no, it's one of ''those''.
:μ This math is cool but it's not about anything that you will ever see or touch, so whatever.
:Σ Thank you for purchasing ''Addition Pro''®!
:Π ...and the ''Multiplication''® expansion pack!
:ζ This math will only lead to more math.
:β There are just too many coefficients.
:α Oh boy, now '''''this''''' is math about something real. This is math that could '''''kill''''' someone.
:Ω Oooh, ''some'' mathematician thinks their function is cool and important.
:ω A lot of work went into these equations and you are going to die here among them.
:σ Some poor soul is trying to apply this math to real life and it's not working.
:ξ Either this is terrifying mathematics or there was a hair on the scanned page.
:γ ''Zoom'' pew pew pew [space noises] ''zoooom!''
:ρ Unfortunately, the test vehicle suffered an unexpected wing separation event.
:Ξ Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.
:ψ You have entered the domain of King Trition, ruler of the waves.

{{comic discussion}}
[[Category:Math]]
[[Category:Language]]